In his statement Dr Fox said: "In repeating a widely-circulated joke, I very much regret if anyone was offended.
He has issued a statement saying he regretted it very much if his joke had caused any offence to anybody.
A spokeswoman for the Spice Girls later said: "One thing is for sure, no one has ever heard of Liam Fox so no one would bother making offensive jokes about him."
'Open racism'
Labour MP had previously said the shadow cabinet member's "open racism" had now become an embarrassment to the Conservative Party.
In his statement Dr Fox said: "In repeating a widely-circulated joke, I very much regret if anyone was offended.
"I naturally apologise if any offence was caused."
Language tests
Labour MP Denis MacShane told BBC News Online: "Liam Fox's covert and now open racism is an embarrassment to the Tories.
"William Hague should have sacked him in the summer after he said foreign doctors should sit language tests.
"Now he makes a racist joke about Mel B and insults every black and Asian creative artist in show business.
"Sigmund Freud said that jokes were the hidden signals about someone's real beliefs."
Mr MacShane added: "Dr Fox needs a long period out of the limelight in order to understand that in the 21st century racist jokes are not acceptable from people in public life."
The Commission for Racial Equality declined to comment on the episode, saying it was a statutory law enforcement agency and did not comment on one-off incidents.